System and method for blind frequency recovery

ABSTRACT

Described herein are systems and methods for accurately estimating and removing a carrier frequency offset. One exemplary embodiment relates to a system comprising a frequency offset detection circuit detecting a carrier frequency offset in an optical signal, and a frequency testing circuit calculating an estimated frequency offset value of the carrier frequency offset, wherein the frequency testing circuit removes a carrier phase based on the estimated frequency offset value and recovers the optical signal. Another exemplary embodiment relates to a method comprising detecting a carrier frequency offset in an optical signal, calculating an estimated frequency offset value of the carrier frequency offset, removing a carrier phase based on the estimated frequency offset value, and recovering the optical signal.

PRIORITY CLAIM/INCORPORATION BY REFERENCE

This application is a Continuation application of U.S. patentapplication Ser. No. 13/048,630, now U.S. Pat. No. 9,042,741, issued onMay 26, 2015, filed on Mar. 15, 2011 entitled “System and Method forBlind Frequency Recovery”. The entire disclosure of this priorapplication is considered as being part of the disclosure of theaccompanying applications and hereby expressly incorporated by referenceherein.

BACKGROUND

Within digital and optical communications systems, a carrier frequencyoffset may refer to a difference between the carrier frequency at atransmitter and the carrier frequency at the receiver. For instance, thetransmitter may transmit at the nominal carrier frequency. At thereceiver, an unmodulated frequency may be required for reception of thetransmission, however it may not be physically possible to have thecarrier frequency at the receiver exactly match the carrier frequency atthe transmitter. Thus, this offset between frequencies may be describedas the carrier frequency offset. Causes for this offset may includetemperature change, mechanical vibration and etc. Accordingly, reductionof the carrier frequency offset through frequency and phase tracking(e.g., frequency recovery) may greatly improve the overall performanceof the digital communications system.

Typically, a carrier recovery system may be used to estimate andcompensate for frequency and phase differences between a carrier wave ofa received signal and a local oscillator of the receiver for the purposeof coherent demodulation. While carrier recovery may be accomplishedwith an optical phase-locked loop (“PLL”), these methods are verycomplex. Conventional digital PLL-based blind carrier recoveryalgorithms have the capability to recover carrier phase and frequencysimultaneously, and thus, is widely used for wireless systems. However,these types of algorithms cannot be used for high-speed optical system.

Unlike the wireless system in which the frequency and phase offsetchanges are relatively similar and slow, the characteristics offrequency and phase offsets in the optical system are very different.For example, frequency change is relatively slow (e.g., typically in themilliseconds for high-quality lasers) but the range may be large (e.g.,more than 100 MHz), while the carrier phase varies much faster ascompared to the wireless systems (e.g., within the nanosecond). Suchcharacteristics will make PLL-based algorithms perform poor due to theintrinsic feedback delay. Furthermore, optical systems typically requireheavily parallel processing that may further degrade the performance ofthese PLL-based algorithms.

SUMMARY

Described herein are systems and methods for accurately estimating andremoving a carrier frequency offset. One exemplary embodiment relates toa system comprising a frequency offset detection circuit detecting acarrier frequency offset in an optical signal, and a frequency testingcircuit calculating an estimated frequency offset value of the carrierfrequency offset, wherein the frequency testing circuit removes acarrier phase based on the estimated frequency offset value and recoversthe optical signal.

Another exemplary embodiment relates to a method comprising detecting acarrier frequency offset in an optical signal, calculating an estimatedfrequency offset value of the carrier frequency offset, removing acarrier phase based on the estimated frequency offset value, andrecovering the optical signal.

A further exemplary embodiment relates to a circuit comprising adetecting means detecting a carrier frequency offset in an opticalsignal, a calculating means calculating an estimated frequency offsetvalue of the carrier frequency offset, a phase removal means removing acarrier phase based on the estimated frequency offset value, and asignal recovering means recovering the optical signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an illustration of the basic structure of carrier recoveryfor an optical system according to an exemplary embodiment describedherein.

FIG. 2 shows an illustration of a first embodiment of a carrierfrequency offset detection system according to systems and methodsdescribed herein.

FIG. 3 shows an exemplary graph including the calculated mean squareerror versus test frequencies at 1 MHz frequency step according to anexemplary embodiment.

FIG. 4 shows an illustration of a second embodiment of a carrierfrequency offset detection system according to systems and methodsdescribed herein.

FIG. 5 shows an illustration of a third embodiment of a carrierfrequency offset detection system according to systems and methodsdescribed herein.

FIG. 6 shows an illustration of a further embodiment of a carrierfrequency offset detection system according to systems and methodsdescribed herein.

FIG. 7 shows an exemplary method for accurately estimating and removinga carrier frequency offset according to an exemplary embodimentdescribed herein.

DETAILED DESCRIPTION

The exemplary embodiments described herein may be further understoodwith reference to the following description and the related appendeddrawings, wherein like elements are provided with the same referencenumerals. The exemplary embodiments are related to systems and methodsfor accurately estimating and removing a carrier frequency offset.

The exemplary systems and methods described herein provide for amulti-stage blind frequency search process for a universal blind carrierfrequency recovery method for a coherent receiver. As will be describedbelow, the coherent receiver may employ any type of modulation format,such as an arbitrary quadrature amplitude modulation (“QAM”) format, apolarized-multiplexed QAM format, etc. The exemplary embodiments mayaccurately estimate the carrier frequency offset by using only tens ofcontinuous symbols, and therefore may be implemented with either aparallel processing-based architecture or a sequential processing-basedarchitecture. While the parallel processing architecture may allow forrelatively faster carrier frequency recovery, the sequential processingarchitecture may allow for very hardware-efficient carrier frequencyrecovery. Furthermore, by using a combination of both the parallel andsequential processing architectures, the tracking speed as well ashardware-efficiency may therefore be adjusted in order to meet the needsof different system applications.

In order to meet the growing capacity demands in the core opticalnetwork, spectrally efficient techniques, such as digital coherentdetection may be implemented. While these techniques allow the use ofadvanced modulation formats (e.g., QAM-modulated systems), high orderQAM modulation formats, such as M>4, have smaller tolerance towardfrequency and phase noise due to decreases in the Euclidian distance,and thus require more robust frequency and phase tracking (e.g., carrierrecovery). Although frequency and phase tracking may be realized byusing training based algorithms, these algorithms require extra overheadand thus reduce the achievable spectral efficiency (“SE”). On the otherhand, blind carrier recovery does not require overhead and may be moreattractive for an optical system.

For optical systems, most of the proposed carrier recovery algorithmsmay only be applicable to phase-shift-keying (“PSK”) systems. Forinstance, a fast Fourier transform (“FFT”) based carrier frequencyrecovery algorithm may be extended from a PSK system to a high-order QAMsystem, but the required FFT size would be very large. An improvedalgorithm may be created by proposing a ring-based classification anddown-sampling method that can significantly reduce the required FFTsize. Accordingly, this improved method may provide a solution for acontinuously operational receiver using a high-quality laser (e.g., suchas external cavity lasers) with very slow frequency noise. However, thismethod may not be used for a system using lasers having fast frequencynoise, such as some distributed Bragg reflector (“DBR”) lasers. Evenwith such high-quality lasers, there exists a need for fast carrierrecovery for a fully dynamic optical network, wherein fast wavelengthprovisioning may be necessary, or for an optical packet networkrequiring burst-mode receivers. The exemplary embodiments describedherein provide a more universal blind carrier recovery technique withina variety of networks and applications.

FIG. 1 shows an illustration of the basic structure of carrier frequencyrecovery for an optical system 100 according to an exemplary embodimentdescribed herein. As is shown in FIG. 1, carrier frequency recovery 110may include a circuit 115 for the detection of carrier frequency offsetand its removal to achieve efficient carrier phase recovery 120.However, the challenging part is how to accurately estimate the carrierfrequency offset.

According to the exemplary systems and methods, the optical system 100may use a multi-stage based blind frequency search method to detect thecarrier frequency offset. As will be described in greater detail below,this system 100 may utilize a variety of frequency testing components toaccurately estimate carrier frequency offset. Specifically, thesefrequency-testing components may use a small number of symbols (e.g., onthe order of only tens of symbols), which may only account fornanoseconds for the high-speed optical system 100. Therefore, the numberof symbols used is much less than any conventional carrier recoveryalgorithm, wherein thousands of symbols are typically required toachieve a reliable carrier frequency. Thus, if the exemplary method isrealized by using a parallel processing-based architecture, very fastcarrier frequency recovery may be achieved. In addition, since theexemplary method may only need a short piece of data information forcarrier frequency offset extraction, it may also be implemented with asequential processing architecture to achieve very hardware-efficientcarrier frequency recovery. By using a combination of parallel andsequential processing architecture, the tracking speed as well ashardware-efficiency can therefore be adjusted to meet the needs ofdifferent system applications.

FIG. 2 shows an illustration of a first embodiment of a carrierfrequency offset detection system 200 according to systems and methodsdescribed herein. As shown in FIG. 2, a two-stage based blind frequencysearch method may be utilized with a parallel processing architecture.The two stages may include a coarse frequency search stage 210 and afine frequency search stage 220. For descriptive purposes, “X₁, X₂, . .. X_(K)” may denote the received modulated signal samples afterequalization (e.g., one sample per symbol) to be used for frequencyoffset detection. In addition, “K” denotes the data block length, and“f₁, f₂, . . . f_(n)” denotes the N different test frequencies used inthe first coarse frequency search stage 210. According to the exampledepicted in FIG. 2, if the allowable maximum carrier frequency offset isF_(max), then the test frequency f_(k) that is used for the coarsefrequency recovery may be selected as:f _(k) =F _(max) +kΔF,Wherein ΔF is the coarse frequency resolution, and k is an integernumber taken from 0 to the nearest integer number closest to F_(max)/ΔF.

For each frequency test unit, the K received signal samples are rotatedby a phase angle given by −2πf_(k)t wherein t denotes the sampleinstant. Accordingly, such a phase rotation operation may remove thefrequency offset if the tested frequency f_(k) is equal to the actualfrequency offset. The phase-rotated signal may then go through a phaserecovery stage to remove the carrier phase and recover the originalsignal (e.g., in a best effort). The exemplary phase recovery stage mayinclude either a single-stage based blind phase search (“BPS”) method230 or a multi-stage hybrid BPS and maximum likelihood (ML) method inorder to remove the carrier phase.

Furthermore, a mean square error may then calculated by:

$\frac{\sum\limits_{i = 1}^{K}{{X_{k} - X_{k}^{D}}}^{2}}{K}$wherein X_(k) ^(D) denotes the decided signal. By using the parallelprocessing depicted in FIG. 2, each of the N frequencies may be testedat the same time and the N output mean square errors may then becompared. The test frequency that gives the minimum mean square errorvalue may output to the next fine frequency search stage. For the finefrequency search stage 220, the M fine test frequencies may be chosen asf_(n)=f_(min) ^(c)+Δf_(n) wherein Δf_(n) is given by:

${\Delta\; f_{n}} = {{{- 0.5}\Delta\; F} + {n\;\frac{\Delta\; F}{M}}}$Wherein n is an integer number taken from [0,M]. The mean square errorscalculated from the M fine test frequencies may be compared and the testfrequency that gives the minimum mean square error value may bedetermined as the final estimated frequency offset. Specifically, anexemplary circuit within the system 200 may perform the calculations andestimations of the frequency offset.

FIG. 3 shows an exemplary graph 300 including the calculated mean squareerror versus test frequencies at 1 MHz frequency steps according to anexemplary embodiment. As shown in FIG. 3, the Y-axis includes normalizedmean square error while the X-axis includes the test frequencies at 1MHz frequency step using different number of continuous data symbolsbased on a 10.7 Gbaud 36 QAM experimental result.

The graph 300 of FIG. 3 represents the results of a 107 Gb/s PDM-36QAMtransmission experiment using external excavity lasers having alinewidth of ˜100 kHz as the laser sources. In order to observe theallowable minimum data length and the allowable maximum coarse frequencysearch step (e.g., resolution), the graph 300 illustrates the calculatedmean square error versus test frequencies at 1 MHz frequency steps usinga different number of continuous data symbols (e.g., block length) for a10.7 Gbaud 36QAM experiment operating with an optical signal-to-noiseratio (“OSNR”) of 20.3 dB, corresponding to a BER of 1.3e⁻³. It can beseen that by using 64 continuous data symbols with a coarse frequencyresolution of about 20 MHz and a fine frequency resolution 1 MHz,reliable carrier recovery may be achieved to within 1-2 MHz.Accordingly, estimating the frequency offset to within 2 MHz allows forvery efficient carrier phase recovery. If the maximum carrier frequencyoffset is controlled to be below 200 MHz, such as some commercialproducts, the proposed two-stage blind frequency search systems andmethods may only need to test a small number (e.g., about 40) ofdifferent frequencies by using the above introduced two-stage frequencysearch technique. Furthermore, the required number of test frequenciesmay be further reduced by introducing additional cascaded stages. Forinstance, if a frequency step of 20 MHz is selected for the first stage,a frequency step of 5 MHz is selected for the second stage and afrequency step of 1 MHz is selected for the final fine-tuning stage,then the required number of test frequencies may be reduced from 40 to29.

Since the data length for detecting carrier frequency offset (e.g., K)may be small (on the order of tens of symbols), the parallel processingembodiment of the frequency offset detection method may be much fasterthan any of the known carrier frequency recovery methods, such as theFFT-based methods discussed above. Accordingly, the parallel processingembodiment may be of significant use to system applications, such as aburst-mode receiver, any continuously operational receiver requiringfast acquisition time, etc.

FIG. 4 shows an illustration a second embodiment of a carrier frequencyoffset detection system 400 according to systems and methods describedherein. The exemplary system 400 may include a single frequency testunit 410, a frequency table 420, a timing control 430, an on/off switch440, and a plurality of registers 450.

Unlike the previous parallel processing architecture, detailed in thesystem 200 of FIG. 2, where the number of frequency test units is equalto the number of the used test frequencies, the system 400 may utilizethe single frequency test unit 410. Furthermore, the mean square errorsof different test frequencies may be calculated sequentially, atdifferent time slots, by using the same frequency test unit 410. Thisexemplary sequential design may dramatically reduce the requiredhardware complexity due to a significant reduction in the amount ofmultiplier operations. An exemplary circuit within the system 400 mayperform the calculations and estimations of the frequency offset.

Although this sequential processing architecture may use additionalmemory and a timing control unit, the complexity of the implementationis much less than that of the extra multiplier operation used in theparallel processing architecture of system 200. Accordingly, theexemplary system 400 depicted in FIG. 4 may use fewer components (e.g.,complementary metal-oxide-semiconductor (“CMOS”) gates, etc.) than theparallel processing architecture of the system 200. Thus, the system 400may be described as very efficient in terms of its hardware design,although its frequency tracking speed may be reduced. Therefore, thesequential processing embodiment illustrated in FIG. 4 may be ofsignificant use in a continuously operational receiver that does notrequire fast acquisition.

FIG. 5 shows an illustration a third embodiment of a carrier frequencyoffset detection system 500 according to systems and methods describedherein. The exemplary system 500 may include a plurality of parallelcarrier frequency test units 510, a frequency table 520, a timingcontrol 530, an on/off switch 540, and a plurality of registers 550.

As shown in FIG. 5, the exemplary system 500 utilizes a combination ofthe parallel processing architecture with the sequential processingarchitecture. The system 500 may provide a carrier recovery circuitdesign with various frequency tracking speed, and hardware-efficiency,that falls between the parallel processing structure of the system 200and the sequential processing structure of the system 400. An exemplarycircuit within the system 500 may perform the calculations andestimations of the frequency offset.

FIG. 6 shows an illustration a further embodiment of a carrier frequencyoffset detection system 600 according to systems and methods describedherein. The exemplary system 600 may include a single frequency andphase test unit 610, a frequency and phase tables 620, a timing control630, an on/off switch 640, and a plurality of registers 650.

As shown in FIG. 6, the system 600 employs a single frequency and phasetest unit in order to calculate the mean square errors of different testfrequencies and test phases. The estimated carrier offset may then bethe test frequency that gives the minimum mean square error. For thecase that the phase recovery is achieved by using blind phase searchbased methods, the hardware implementation efficiency may be furtherimproved by using the architecture of the system 600, as depicted inFIG. 6. An exemplary circuit within the system 600 may perform thecalculations and estimations of the frequency offset.

FIG. 7 shows an exemplary method 700 for accurately estimating andremoving a carrier frequency offset according to an exemplary embodimentdescribed herein. It should be noted that method 700 will be discussedwith reference to various exemplary systems and components describedabove.

It should be noted that the exemplary method may be stored as a set ofinstructions or software code on a non-transitory computer readablestorage medium, such as a computer memory. This set of instructions maybe executable by a processor and may be operable at least to perform thesteps of the exemplary method 700 depicted in FIG. 7.

Beginning with step 710, a frequency offset detection circuit may detecta carrier frequency offset in an optical signal. As noted above, thefrequency offset detection circuit may utilize digital coherentdetection to detect the carrier frequency offset.

In step 720, a frequency testing circuit may calculate an estimatedfrequency offset value of the carrier frequency offset. Specifically,the frequency testing circuit may utilize one or more frequency testingunits, depending on the architecture of the system. In the event thesystem includes a parallel processing architecture, the frequencytesting circuit may determine a minimum mean square error for each ofthe multiple tests simultaneously. In the event the system includes asequential processing architecture, the frequency testing circuit maydetermine a minimum mean square error for each of the multiple tests atdifferent intervals. In the event the system includes a combinationprocessing architecture, the frequency testing circuit may use anycombination of tests described above.

In step 730, the frequency testing circuit may utilize a first coarsefrequency search stage for multi-stage frequency search techniques. Asnoted above, the frequency testing circuit may calculate mean squareerror versus test frequencies at a coarse frequency resolution of about20 MHz frequency step using different number of continuous data symbols(i.e. block length). The frequency testing circuit may compare theresults of the coarse frequency search and the test frequency thatprovides the minimum mean square error may be output to the next finefrequency search stage in step 740.

In step 740, the frequency testing circuit may utilize a next finefrequency search stage for multi-stage frequency search techniques. Asnoted above, the frequency testing circuit may calculate mean squareerror versus test frequencies at a fine frequency resolution of about 1MHz frequency steps using different number of continuous data symbols(i.e. block length). The frequency testing circuit may compare theresults of the fine frequency search and the test frequency thatprovides the minimum mean square error may be final estimated carrierfrequency offset to be used in step 750.

In step 750, the frequency testing circuit may remove a carrier phasebased on the estimated frequency offset value in order to recover theoptical signal. As described above, the frequency testing circuit mayremove a carrier phase using a phase rotation operation to generate aphase rotated signal.

Intradyne detection-based digital coherent receivers may allow for thecarrier frequency of the received signal source different from the localoscillator while avoiding the need for complex optical phase locked loop(“PLL”) in the optical system. As noted above, such a frequency offsetmay be estimated and removed in the digital domain (e.g., digitalcarrier frequency recovery) by way of any of the exemplary embodimentsdescribed herein.

As detailed above, these embodiments provide a multi-stage based blindfrequency search method to accurately estimate the carrier frequencyoffset and remove the frequency offset. These embodiments may beimplemented either with parallel processing based architecture toachieve very fast carrier frequency recovery, or with a sequentialprocessing architecture to maximize hardware-efficient during carrierfrequency recovery. Furthermore, a combination of parallel andsequential processing may be implemented in order to customize thetracking speed, as well as hardware-efficiency, to meet the needs ofdifferent system applications. For example, a burst-mode receiver mayrequire very fast carrier recovery of the parallel embodiment while thenormal continuous-operational receiver with high-quality laser may allowfor relatively slow frequency recovery of the sequential embodiment.Furthermore, each of the embodiments described herein may be applicableto any modulation formats, such as QAM or polarization-multiplexed QAM,and for arbitrary frequency offset.

According to the exemplary methods and systems described above, digitalcoherent detection combined with the use of high-order QAM is anadvantageous technique for achieving high-spectral efficiency opticaltransmission at a data rate beyond 100-Gb/s. In addition to higher speedand higher spectral efficiency, future optical networks may also requirefast receiver acquisition time to provide fast wavelength provision.Furthermore, statistical multiplexing based optical packet network maybe needed in the future transport network. For these advanced opticalnetworks, fast carrier recovery in the coherent receiver is criticalimportant.

Accordingly, the exemplary embodiments propose a blind carrier frequencyrecovery technique that may be used in these advanced optical networksfor arbitrary modulation formats and having any frequency offset.Moreover, the exemplary embodiments not only can be implemented withparallel processing to achieve very fast frequency tracking speed, theymay also be implemented with sequential processing to achieve very goodhardware efficiency. By using a combination of parallel processing andsequential processing, different tracking speed, as well as hardwareefficiency, may be realized by the various embodiments described aboveto meet the needs of different applications. Thus, the exemplaryembodiments may provide universal carrier frequency recovery for anycoherent receiver.

It will be apparent to those skilled in the art that variousmodifications may be made the exemplary embodiments, without departingfrom the spirit or the scope of the systems and methods describedherein. Thus, it is intended that the exemplary embodiments covermodifications and variations of these systems and methods provided theycome within the scope of the appended claimed and their equivalents.

What is claimed is:
 1. A system, comprising: a frequency offsetdetection circuit configured to detect a carrier frequency offset in anoptical signal; and a frequency testing circuit configured to calculatean estimated frequency offset value of the carrier frequency offset by:generating a coarse phase error frequency based on rotating a pluralityof samples of the optical signal by a corresponding one of a pluralityof phase angles and selecting one of the plurality of phase angleshaving a lowest mean square error value as the coarse phase errorfrequency; generating a plurality of fine test frequencies by applying aplurality of offsets to the coarse phase error frequency, the fine testfrequencies being dispersed throughout a desired range of fine testfrequencies, each of the fine test frequencies being separated from anadjacent one of the fine test frequencies by an interval determinedbased on a predetermined quantity of the fine test frequencies, andselecting as the estimated frequency offset value, one of the fine testfrequencies based on a mean square error, wherein the frequency testingcircuit is configured to remove a carrier phase from the optical signalbased on the estimated frequency offset value to recover the opticalsignal.
 2. The system of claim 1, wherein the frequency offset detectionincludes a parallel processing architecture for multi-stage frequencydetection.
 3. The system of claim 2, wherein the parallel processingarchitecture includes a plurality of frequency testing units performingmultiple tests simultaneously, and the frequency testing circuit isconfigured to determine the mean square error for each of the multipletests simultaneously.
 4. The system of claim 1, wherein the frequencyoffset detection includes a sequential processing architecture forsingle-stage frequency detection.
 5. The system of claim 4, wherein thesequential processing architecture includes a single frequency testingunit and the frequency testing circuit is configured to determine themean square error for each of multiple tests at different intervals. 6.The system of claim 1, wherein the frequency offset detection circuitincludes a combination architecture having a parallel processingarchitecture and a sequential processing architecture for multi-stagefrequency detection.
 7. The system of claim 1, wherein the opticalsignal is used to transport data in a statistical multiplexing basedoptical packet network.
 8. The system of claim 1, wherein the estimatedfrequency offset value is determined based on 64 continuous datasymbols.
 9. The system of claim 1, wherein 40 fine test frequencies aregenerated.
 10. The system of claim 1, wherein 29 fine test frequenciesare generated.
 11. A method, comprising: detecting a carrier frequencyoffset in an optical signal; calculating an estimated frequency offsetvalue of the carrier frequency offset by generating a coarse phase errorfrequency based on rotating a plurality of samples of the optical signalby a corresponding one of a plurality of phase angles and selecting oneof the plurality of phase angles having a lowest mean square error valueas the coarse phase error frequency and generating a plurality of finetest frequencies by applying a plurality of offsets to the coarse phaseerror frequency, the fine test frequencies being dispersed throughout adesired range of fine test frequencies, each of the fine testfrequencies being separated from an adjacent one of the fine testfrequencies by an interval determined based on a predetermined quantityof the fine test frequencies, and selecting, as the estimated frequencyoffset value, one of the fine test frequency based on a mean squareerror; removing a carrier phase from the optical signal based on theestimated frequency offset value; and recovering the optical signal. 12.The method of claim 11, wherein the carrier frequency offset detectionincludes parallel multi-stage frequency detection.
 13. The method ofclaim 12, wherein the parallel multi-stage frequency detection includesperforming multiple tests simultaneously and determining the mean squareerror for each of the multiple tests simultaneously.
 14. The method ofclaim 11, wherein the carrier frequency offset detection includessequential single-stage frequency detection.
 15. The method of claim 14,wherein the sequential single-stage frequency detection and determiningthe mean square error for each of multiple tests at different intervals.16. The method of claim 11, wherein the carrier frequency offsetdetection includes parallel multi-stage frequency detection andsequential single-stage frequency detection.
 17. The method of claim 11,wherein the optical signal is used to transport data in a statisticalmultiplexing based optical packet network.
 18. A circuit, comprising: acalculation component that calculates an estimated frequency offsetvalue of a carrier frequency offset by generating a coarse phase errorfrequency based on rotating a plurality of samples in an optical signalby a corresponding one of a plurality of phase angles and selecting oneof the plurality of phase angles having a lowest mean square error valueas the coarse phase error frequency and generating a plurality of finetest frequencies by applying a plurality of offsets to the coarse phaseerror frequency, the fine test frequencies being dispersed throughout adesired range of fine test frequencies, each of the fine testfrequencies being separated from an adjacent one of the fine testfrequencies by an interval determined based on a predetermined quantityof the fine test frequencies, and selecting, as the estimated frequencyoffset value, one of the fine test frequencies based on a mean squareerror.
 19. The circuit of claim 18, further comprising: a detectioncomponent that detects the carrier frequency offset in an opticalsignal; a phase removal component that removes a carrier phase from theoptical signal based on the estimated frequency offset value; and asignal recovery component that recovers the optical signal.
 20. Thecircuit of claim 19, wherein the detection component includes one of aparallel processing architecture for multi-stage frequency detection, asequential processing architecture for single-stage frequency detection,and a combination architecture for multi-stage frequency detection.